A project requires 850 cubic yards of fill material with 95% compaction. If the soil has a shrinkage factor of 15%, how many cubic yards of loose soil must be hauled to the site?
Correct Answer
C) 1000 cubic yards
With 15% shrinkage, you need 850 ÷ 0.85 = 1000 cubic yards of loose soil to achieve 850 cubic yards of compacted fill at 95% compaction.
Why This Is the Correct Answer
When soil is compacted, it shrinks by 15%, meaning the final compacted volume is only 85% of the original loose volume. To find the required loose soil volume, we divide the needed compacted volume by the compaction factor (0.85). The calculation is 850 ÷ 0.85 = 1000 cubic yards. The 95% compaction requirement is already factored into the 850 cubic yards specified, so we only need to account for the 15% shrinkage.
Why the Other Options Are Wrong
Option A: 977.5 cubic yards
This answer incorrectly multiplies 850 by 0.85 instead of dividing by 0.85, which would give you less material than needed rather than accounting for the shrinkage that requires more loose material.
Option B: 722.5 cubic yards
This answer incorrectly adds 15% to the required volume (850 × 1.15), which is the wrong mathematical approach for dealing with shrinkage factors in soil compaction calculations.
Memory Technique
Remember 'Shrinkage = Shortage' - when soil shrinks, you have a shortage, so you need to START with more loose material. Always divide by the remaining percentage (100% - shrinkage%).
Reference Hint
Look up soil compaction and earthwork calculations in Chapter 7 (Site Work) or the earthwork section of your construction reference manual.
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